Here is the full list of all 21 Touhou Mystery Reel achievements.
Perfectly counter Reimu's aerial attacks several times
Get the last hit of Reimu immediately after she falls
Defeat Reimu
Make the chicken soup
Gain friendliness of the fortune cat
Clear Youmu's training
Completely defeat Motoori Kosuzu
Make Motoori Kosuzu step on the banana
Clear stage 1 and complete the mission
Defeating Motoori Kosuzu
Help little fairy
Some things should not be done
Complete Flandre's rehearsal
Complete Sakuya's challenge
Open the game at least once